Definitely report it to Sainsburys. I've done this several times (not for Sainsburys in particular, for several different companies!) & have had mixed results but frequently good ones.
One of my letters c&ped from the Other Place (
http://www.anothercyclingforum.com/index.php?topic=19866.0 )
"I have a complaint about one of your drivers - in a BT
Openreach van, registration [reg number of van].
I was cycling east along Southwark Park Road (London SE16), around 1745
today (Tue 20 Nov), when your driver overtook me at high speed and far
too close - around a foot from my right shoulder.
This was just east of the junction with Dunton Road. The road is wide
here and there is plenty of room for safe overtaking - and in any case
if there is not room to overtake safely and with appropriate space, the
driver should not have done so.
The Highway Code states that drivers should give cyclists plenty of room
when overtaking (rule 212) and at least as much space as you would give
a car (rule 163).
My experience is that the majority of professional drivers are safe and
courteous. I am sure that you would not wish your drivers to have a
lower standard.
I would appreciate it if you would bring this to the attention of the
driver concerned, and take appropriate action to ensure improved driving
standards in future."
(got a phone call, apology, & IIRC promise to have a chat to all drivers, from that one.)